Degeneracy and Correlation in Neutrino Oscillation Parameters Hisakazu Minakata Tokyo Metropolitan...
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Degeneracy and Correlation in Neutrino Oscillation Parameter
s
Degeneracy and Correlation in Neutrino Oscillation Parameter
s
Hisakazu MinakataTokyo Metropolitan University
Hisakazu MinakataTokyo Metropolitan University
May. 2-6, 2006 SNOW@Stockholm
A machinery in my talk
Oscillation probability draw ellipse if plotted in bi-P plane
Role played by CP phase and the matter clearly distinguished
Art work by Adam Para Art work by Adam Para
Two solutions of S232 xTwo solutions of S23
2 x
May. 2-6, 2006 SNOW@Stockholm
Cause of the degeneracy; easy to understand
• You can draw two ellipses from a point in P-Pbar space
• Intrinsic degeneracy
• Doubled by the unknown sign of m2
• 4-fold degeneracy
May. 2-6, 2006 SNOW@Stockholm
23 octant degeneracy
Pe= sin2213 x s223
Pe= sin2213 x s223
Solar m2 on
Matter effect on
Solar m2 on
Matter effect on
OY Nufact03OY Nufact03
Altogether 8-fold degeneracyAltogether 8-fold degeneracy
May. 2-6, 2006 SNOW@Stockholm
Structure of intrinsic & sign-m2 degeneracy in (matter) perturbative regime
• Intrinsic degeneracy;
• sign(m2)- degeneracy arises because P is approx. invariant under:
m2 m2
T2K IIT2K II
MN JHEP01MN JHEP01
May. 2-6, 2006 SNOW@Stockholm
General comments• Degeneracy occurs because of the lack of
information, e.g., P, Pe and Pe-bar at a particular energy
• Therefore, it can be resolved by adding information easy for theorists
• Practically, however, NOT an easy task to carry out experimentally
• Discussion cannot be purely “theoretical” and has to involve “feasibility of the measurement” you propose, and “practicality of the experiments” No unique
answer !
No unique answer !
May. 2-6, 2006 SNOW@Stockholm
Possible alternative strategies toward the resolution
• Conceptually simple• Probably require
multiple detectors/settings
• Inevitable if 3 types of degeneracy tightly couple with each other
• More practical and experimentalists friendly
• Has to show that one can do the job one by one
Everything at once approachEverything at once approach
One by one resolution approachOne by one resolution approach
May. 2-6, 2006 SNOW@Stockholm
General comments (continued)
• Lifting sign-m2 degeneracy requires matter effect long baseline => \gsim 1000 km required
• intrinsic degeneracy can be efficiently resolved by spectrum information
• Generally speaking,23 octant degeneracy tends to decouple from others
• many ideas welcome
Exception: m2(ee) - m2() methodException: m2(ee) - m2() method
alternative ways ?alternative ways ?
May. 2-6, 2006 SNOW@Stockholm
factory as ultimate degeneracy solver
• By combining at 3 detectors at 130, 730, and 2810 km, it was claimed that neutrino factory can resolve all the 8-fold degeneracy if 13 > 1° (Donini, NuFACT03)
Typical everything at once type Typical everything at once type
May. 2-6, 2006 SNOW@Stockholm
Golden + silver NuFact + superbeam
• 1st concrete way that proved to work for resolution of all the degeneracy
• Powerful, work down to 1-2 degree of 13
• Note that Vcb ~ 2 degree • Yet, a bit expensive; • conservatively ~1000 Million Euro/d
egeneracy (rich man’s solution) • Ultimate degeneracy solver, but certainly
not “Mayflower” (unless 13 ~ 1o)
Highly nontrivial!Highly nontrivial!
If NuFACT reached “J-PARC stage” everything changes !If NuFACT reached “J-PARC stage” everything changes !
May. 2-6, 2006 SNOW@Stockholm
Anatomy of degeneracy
• To make real progress, it is important to have a systematic understanding of the nature of degeneracy
• Need concrete framework to analyze the question
• 1st order in matter perturbation theory plus corresponding appropriate experimental setting;
• T2K II or T2KK(Kamioka-Korea) Ishitsuka et al. 05 Ishitsuka et al. 05
May. 2-6, 2006 SNOW@Stockholm
Let’s start from the intrinsic degeneracy
• degenerate solution at VOM:
13(2) = 13
(1)
T2K IIT2K II
Spectrum analysis should be powerful !
Spectrum analysis should be powerful !
May. 2-6, 2006 SNOW@Stockholm
Spectral information IS powerful(almost) resolve intrinsic degeneracy at sin2213=0.01(almost) resolve intrinsic degeneracy at sin2213=0.01
T2K II (from 1000 page Ishitsuka file) T2K II (from 1000 page Ishitsuka file)
SK momentum resolution ~30 MeV at 1 GeVSK momentum resolution ~30 MeV at 1 GeV
May. 2-6, 2006 SNOW@Stockholm
Expected Expected signal, BG and signal, BG and
22 and anti-
×Kamioka and Korea
and anti-×
Kamioka and Korea
5 energy bins5 energy bins
syst. Errors:
5% BG (overall) 5% BG (energy dep.) 5% signal efficiency
syst. Errors:
5% BG (overall) 5% BG (energy dep.) 5% signal efficiency
4yrs + 4yrs anti-sin2213=0.1, =/2
4yrs + 4yrs anti-sin2213=0.1, =/2
signalsignal
BGBG
Kajita in NOVE2006Kajita in NOVE2006
May. 2-6, 2006 SNOW@Stockholm
Sign-m2 degeneracy• Resolution of sign-m2 degen
eracy requires the matter effect
• Requires baseline ~1000 km• 2nd detector seems required t
o go down to sin2213=.02
May. 2-6, 2006 SNOW@Stockholm
It is not quite only the matter effect
• With the same input parameter and Korean detector of 0.54 Mt the sign-m2 degeneracy is NOT completely resolved
2 identical detector method powerful !
2 identical detector method powerful !
May. 2-6, 2006 SNOW@Stockholm
How to solve 23 octant degeneracy
• Detect solar Dm2 term ~c23
2
• Requires baseline ~ earth radius
• well controlled systematic error plus enormous statistics
• Powerful at small 13
• Combining reactor measurement of 13
• Requires great precision in 13 measurement
• Powerful at large 13
• If feasible, “Mossbauer” helps
Strategy: Look for terms which depend on 23 but not through the form s23
2 x sin2213
Strategy: Look for terms which depend on 23 but not through the form s23
2 x sin2213
May. 2-6, 2006 SNOW@Stockholm
[email protected]@NNN05Atm ; powerful way for octant degene.Atm ; powerful way for octant degene.
May. 2-6, 2006 SNOW@Stockholm
Reactor + accelerator method
• Acc-disappearance => s2
23=0.4 or 0.6• Acc-appearance =
> s223sin2213 = 0.
06• Reactor =>
sin2213 = 0.1
• Solves 23 degeneracy
May. 2-6, 2006 SNOW@Stockholm
Region of resolved 23 degeneracy
T2K II (4MW+HK) + phase II type reactorT2K II (4MW+HK) + phase II type reactor
Hiraide et al. (7 samurai) Hiraide et al. (7 samurai)
May. 2-6, 2006 SNOW@Stockholm
Decoupling of the degeneracy
• Suppose that you succeed to solve the particular degeneracy, by forgetting about the remaining ones
• It does NOT necessarily mean that the problem is solved
• You have to verify that your treatment of degeneracy A is valid irrespective of the presence of degeneracy B
• One solution: decoupling between the degeneracy
May. 2-6, 2006 SNOW@Stockholm
23 and sign-m2 degeneracy decouple
• For example, one can show, to first order in matter effect, the followings:
P(octant) = P(1st octant) - P(2nd) is invariant under the interchange of two sign-m2 degenerate pair
P(hierarchy) = P(m2 +) - P(m2 -) is invariant under the interchange of two 23 octant degenerate pair
May. 2-6, 2006 SNOW@Stockholm
Intrinsic degeneracy decouple ?
• Intrinsic degeneracy nearly decouples from the rest
• More importantly, in T2K II setting, it is resolved by spectrum analysis decouple from the game
• Altogether three degeneracies (approximately) decouple with each other in T2K (or T2KK) setting
May. 2-6, 2006 SNOW@Stockholm
Correlation ?• The title of this talk
contains “correlation”. What about that ?
• “correlation” may be incompletely resolved degeneracy
• No continuous degeneracy in Pe
Nufact golden Nufact golden
May. 2-6, 2006 SNOW@Stockholm
No significant “correlation” in T2K II
Spectral information importantSpectral information important
May. 2-6, 2006 SNOW@Stockholm
Many remaining questions • Does beam help ??
• Does monochromatic beam help ??
• To what extent the lower energy threshold of NuFACT change the sensitivity of resolving degeneracy ?
• What would be a powerful supplementary measurement ?
ISS NuFACT ongoing, report expected in Sep. 06
ISS NuFACT ongoing, report expected in Sep. 06
example: 12 for m2ee - m2
methodexample: 12 for m2ee - m2
method
May. 2-6, 2006 SNOW@Stockholm
Conclusion • Nature of the degeneracy well understood
• With T2KK or similar 2 detector settings there appeared a well defined method for lifting intrinsic and sign-m2 degeneracy
• Spectral information solves intrinsic degeneracy and matter effect does sign-m2 degeneracy
• Resolving 23 degeneracy requires solar term or reactor II
• Consistency maintained by “decoupling”